Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 30
... multiply the re- mainder by 2 ; the product will be the number of right angles . Thus , if the number of sides be represented by S , the number of right angles will be represented by ( 2S ' — 4 ) . The Theorem is not varied in case of a ...
... multiply the re- mainder by 2 ; the product will be the number of right angles . Thus , if the number of sides be represented by S , the number of right angles will be represented by ( 2S ' — 4 ) . The Theorem is not varied in case of a ...
Page 45
... multiplied by the perpendicular distance between them . Let ABDC represent any trape- zoid ; draw the diagonal BC , divid- ing it into two triangles , ABC and BCD : CD is the base of one tri- angle , and AB may be considered A E as the ...
... multiplied by the perpendicular distance between them . Let ABDC represent any trape- zoid ; draw the diagonal BC , divid- ing it into two triangles , ABC and BCD : CD is the base of one tri- angle , and AB may be considered A E as the ...
Page 61
... multiplying the magnitudes by the same number . Thus , the products , Am and Bm , are equimultiples of A and B. 11. A ... multiplied and the other is divided by the same number . Thus , if A and B be two magnitudes , so related that when ...
... multiplying the magnitudes by the same number . Thus , the products , Am and Bm , are equimultiples of A and B. 11. A ... multiplied and the other is divided by the same number . Thus , if A and B be two magnitudes , so related that when ...
Page 63
... Multiplying each of these equals by A × C , we have BX CA × D. Hence the theorem ; if four magnitudes are in propor- tion , etc. Cor . 1. Conversely ; If we have the product of two mag- nitudes equal to the product of two other ...
... Multiplying each of these equals by A × C , we have BX CA × D. Hence the theorem ; if four magnitudes are in propor- tion , etc. Cor . 1. Conversely ; If we have the product of two mag- nitudes equal to the product of two other ...
Page 68
... multiplying the first four by the second four , term by term , are also proportional . Admitting that and A : B :: C ... Multiply these equations , member by member , and Or , AX = DN CM3 AX BY :: CM : DN . The same would be true in any ...
... multiplying the first four by the second four , term by term , are also proportional . Admitting that and A : B :: C ... Multiply these equations , member by member , and Or , AX = DN CM3 AX BY :: CM : DN . The same would be true in any ...
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Common terms and phrases
ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROB PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY square straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume
Popular passages
Page 322 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Page 41 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 65 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Page 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.